How to Use bpy.ops.object.add_named()?
This works.
bpy.ops.object.add_named(linked = True, name = &quot;Cube.010&quot;)

I get it now. The name of this function, add_named() is misleading. It's not about adding a new object and naming it as it's created. It's about copying an existing, named, object.
What I was originally looking for was a way to link a copy()ed object to the original so they share data. The idea was to use copy() to make the new object, then it could be either:

linked into a collection as an independent object, or
linked to another object so they share data.

It seemed like a logical assumption to make that a copy()ed object might have these options open.
Still exploring...